Life at the Landau pole

Abstract

If a quantum field theory has a Landau pole, the theory is usually called 'sick' and dismissed as a candidate for an interacting UV-complete theory. In a recent study on the interacting 4d O(N) model at large N, it was shown that at the Landau pole, observables remain well-defined and finite. In this work, I study both relevant and irrelevant deformations of the said model at the Landau pole, finding that physical observables remain unaffected. Apparently, the Landau pole in this theory is benign. As a phenomenological application, I compare the O(N) model to QCD, by identifying ${\Lambda }_{\overline{\mathrm{MS}}}$ with the Landau pole in the O(N) model.

arXiv comment24 pages, 6 figures; v2: typos fixed, slightly expanded discussion; v3: expanded discussion, more typos fixed, matches version accepted for publication

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• Exact quantization conditions and full transseries structures for $\mathcal{P}\mathcal{T}$ symmetric anharmonic oscillators
• Rescuing 331 bileptons from the Landau pole